NSW Police said the outages could be affecting people trying to call triple zero (000) or the Police Assistance Line (131 444).

"The advice we have received indicates Telstra customer mobile phone calls to Triple Zero (000) should automatically be connected via another carrier; however, if you are experiencing problems use a landline," they said in a statement at 12.14pm.

Aussie Outages' live outage map, which shows complaints about network problems across all major capital cities, was reporting more than 10,000 incidents about 10am. Complaints started rolling in on social media about the same time, with hundreds of Telstra customers taking to Twitter to report an inability to phone out.

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Telstra mobile customers are reporting network difficulties across the country.

“We’re disappointed. We don’t like to let our customers down,” he said.

Mr Wright said the network outage was quickly identified by the Telstra system about 10am and by noon the network’s problematic elements were isolated and the network was progressively restored.

By 2.30pm, he was confident a majority of services were restored.

“Anytime we have an event like this, we work day and night to identify what the root cause was and make sure we move quickly to fix what it was,” Mr Wright said.

“Sometimes it's a software fault, sometimes its a bit of hardware so we will be working as quickly as possible.”

Compensation for customers impacted by the outage is unknown and Mr Wright said the company would work with customers on an individual basis.

“We think, in the world we live in today with such generous allowances, [a free data day] probably doesn’t fit where we currently are.”

Mr Wright said calls to triple zero were not affected by the outage.

At 12.55pm, a Telstra spokesman said the company's 4G voice and data traffic volume was continuing to be restored nationally after it bypassed hardware that had been preventing some customers from accessing the 4G mobile network; 3G voice and data volumes were also improving.

"We are working with many of our enterprise and government customers to ensure their services are restored as quickly as possible," he said.

Telstra earlier apologised for the outage, saying: "We are very sorry for the interruption to services, either directly to customers or through business and government services."

By 2pm, daily voice and data traffic on the 3G and 4G networks were "approaching typical daily levels" though some customers still had intermittent issues or delayed call connections.

"We are still investigating the root cause," the spokesman said.

This is one of multiple incidents this month for Australia's biggest telecommunications company, which ran into difficulties in early May after triple zero services were hit by a network issue that prevented people from calling the emergency number across the country.

And on May 1, Telstra had an outage leaving customers across the country unable to make and receive voice calls for about three hours due to an outage on the National Broadband Network and 4G.

Some customers have called for the telco to offer free data days to make up for the inconvenience, an approach Telstra has taken in the past after previous outages, while others are pushing for financial compensation.